{
  "abstract": "We give two-sided moment estimates for decoupled chaoses of any order generated by independent symmetric random variables with regular moment growth: $\\|X\\|_{2p}\\le K\\|X\\|_p$ for every $p\\ge1$. The estimates involve only the coefficient tensor and the one-dimensional tails. They use the partition norms of Adamczak and Latała, with constants depending only on the order and on $K$. The proof starts with log-concave tails. Gaussian smoothing gives the estimate for the expected norm needed for induction, and a product comparison reduces the remaining distributions to this case. The extra tensor indices introduced by the comparison are removed using Rademacher moments. A comparison with products of log-concave-tail variables then extends the formula to regular moment growth. We also give tail bounds and explicit Rademacher and Weibull formulas for $r\\ge1$, including fourth-order examples. This article was developed with the assistance of GPT Astra-6.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05829",
  "author_total": 1,
  "authors": [
    {
      "name": "Rafał Meller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4q2abxyght0a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05829",
  "fulltext_url": null,
  "id": "d4q2abxyght0a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05829",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7220748356",
  "pdf_url": "https://arxiv.org/pdf/2610.05829",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4q2abxyght0a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05829",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05829"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Moment estimates for chaoses with regular moment growth",
  "title_text": "Moment estimates for chaoses with regular moment growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/d4q2abxyght0a",
  "venue": "arXiv",
  "versions": []
}